Maximum likelihood estimation of inflation factors on error covariance matrices for ensemble Kalman filter assimilation

Abstract

AbstractIn the ensemble Kalman filter, the forecast error covariance matrix is estimated as the sampling covariance matrix of the forecast ensemble. However, it is well known that such estimations may be far from the true forecast error covariance matrix. In this paper, an inflation approach on forecast error covariance matrix based on the maximum likelihood estimation theory is developed and compared to an existing time‐dependent inflation method and the best‐tuned constant inflation. Our method was first tested on a 40‐variable Lorenz model using spatially correlated observation errors. Specifically, when the observation error variance is incorrectly specified, our proposed method can simultaneously inflate on both forecast and observation error covariance matrices. We then assessed our approach on the two‐dimensional Shallow Water Equation model with higher state dimensions and a larger correlated observation system. The results confirmed that our method is effective in retrieving the true states and correcting observation error variances. Copyright © 2011 Royal Meteorological Society